Theorem con5i

Description: Inference form of con5 . (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	con5i.1	⊢ ( 𝜑 ↔ ¬ 𝜓 )
Assertion	con5i	⊢ ( ¬ 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		con5i.1	⊢ ( 𝜑 ↔ ¬ 𝜓 )
2		con5	⊢ ( ( 𝜑 ↔ ¬ 𝜓 ) → ( ¬ 𝜑 → 𝜓 ) )
3	1 2	ax-mp	⊢ ( ¬ 𝜑 → 𝜓 )